Numerical and Simplified Analytical Solutions for Typical Spillways - Selected Topics of Computational and Experimental Fluid Mechanics - page 439

Fig. 3 Identification of
coefficient (a)

22

y = 0.0337x + 8.2171x 10 ^6
R² = 0.9836

21

20

19

18

17

16

15

200 250 300 350 400

Reynolds Number, ( x 10 ^ 6)

Fig. 4 Evaluation of
coefficient (a) for the case
A2 indicated in Table 2

x axis, [m]

0 2 4 6 8

0

-5

-10

-15 Eq. 1

CFD
Eq. 2

-20

-25

was compared with Eq. 1 and the numerical solution, presenting the results in Fig. 4 .
The comparison shows that Eq. 2 significantly enhances the prediction and proves
that an additional coefficient reduces the effort demanded in an evaluation of several
scenarios through numerical solutions for a spillway with the same characteristics in
the design.
Investigations related to the implementation of Eq. 2 for a set of numerical solu-
tions with spillways of different characteristics in the design requires further analysis.
For instance differences in a set of spillways with a marked difference in the slope
of the wall at the upstream or downstream side of the spillway may affect the water
flow behavior significantly.

4 Conclusions

This work presents a proposal to evaluate the predicted water fall profile for a spill-
way with no slope at any of the two faces. The modification in a simplified analytical
equation consists only in the addition of the (Re) and an associated coefficient (a)
as parameters that can include all the phenomena happening in a spillway water
fall under turbulent conditions. The coefficient (a) will be reliable within a regime
of operation of the spillway previously evaluated through numerical solutions. The
inclusion of the coefficient (a) does not increase the difficulty in quick calcula-